# Expection of Angular Momentum

1. Nov 11, 2009

### wam_mi

1. The problem statement, all variables and given/known data

I am trying to calculate the expectation of the y-component of the angular momentum L.
$<L_{y}>$. How should I approach this?

2. Relevant equations

I try to write it in terms of the following commutator

$L(y) = \frac{2*pi}{ih} [L_{x}, L_{z}]$

3. The attempt at a solution

2. Nov 11, 2009

### Avodyne

What do you know about the state in which you are to take the expectation value?

3. Nov 11, 2009

### wam_mi

Hi there, the state is given as |l, m>, where l is the orbital angular momentum quantum number, and m is the magnetic moment quantum number.

I want to prove that to compute <l,m| L(y) |l,m> = <L(y)> =0, how should I approach this?

Many thanks!

4. Nov 11, 2009

### gabbagabbahey

If I were you, I'd write $L_y$ in terms of the raising and lowering operators $L_{\pm}$...

5. Nov 11, 2009

### wam_mi

Hi there, thank you for your reply.
I was told that I have to use the commutation relation between the L(x) and L^2 to get the expectation value of L(y). How can I do that though?

Thanks

6. Nov 11, 2009

### gabbagabbahey

I'm not sure...the only way I know of showing it is to use the raising and lowering operators.

You seem to be working on basically the exact same problem as jazznaz in this thread, so maybe you two should work together and see what you can come up with.